Electronic halftone generator

ABSTRACT

Method and apparatus for scanning a document original, either black and white or color, and reproducing a corresponding halftone reproduction thereof either locally or at a remote location. A halftone signal is generated by pulse width modulating or comparing the scanned, or video, signal with a periodic signal having two frequencies and phases to create a dot pattern output which is a function of the frequency and phase of the two combined modulating signals. The halftone reproduction generated has variable dot configurations that are controllable to enable both rotation of the dot pattern (screen angle) and geometric modifications of the dot pattern. If the document original is in color, light of three different colors is caused to scan the document, each resultant video signal being processed in a manner as set forth hereinabove. In a preferred embodiment, different screen angles are utilized for each color that comprises the reproduction.

This is a continuation of application Ser. No. 688,669, filed May 21,1976, now U.S. Pat. No. 4,149,183.

BACKGROUND OF THE INVENTION

The printing process commonly used in industries which requirereproducing graphic material, the newspaper and book publishingindustries, for example, deposits a uniform density of ink on paperwhenever it is desired to print all or a portion of an image anddeposits no ink when the absence of an image is desired.

The all or nothing process poses no problem when alphabetical or otheralphanumeric characters are printed. However, when pictures such asphotographs are printed, the problem of reproducing the continuous tones(i.e. light gradations) arises. This problem has been solved bytransforming the continuous tones in the original image into a halftoneimage which comprises a large number of ink dots of various sizes. Thisis referred to as "screening" and is performed by projecting the imagethrough a fine mesh screen onto a photographic medium. When the largestdots and the spaces on the paper between the dots are made smallcompared with the visual acuity of the human eye, the dots and thespaces between the dots fuse visually in the screened image, the eyebelieving it is seeing continuous tones.

However, in an automated system in which electronic image reproductionforms at least part of the process of converting a continuous originalimage into a halftone image, the necessity for switching from electronicto photographic techniques in order to produce halftone is a factorwhich adds to the cost and complexity of the process. An electronicphotocomposition system which obviates this problem is disclosed in U.S.Pat. No. 3,465,199. The system disclosed therein translates the tonalinformation on an original transparency into a corresponding image onthe face of a cathode ray tube. The halftone images are recorded on filmand thereafter may be processed into a printing plate by well knowntechniques. Another system which eliminates the aforementionedphotographic technique is disclosed in U.S. Pat. No. 3,646,262 whichalso discloses means to vary the size or shape of the halftone dotsformed on a photo-sensitive member. The aforementioned systems areprimarily concerned with reproducing, as halftone, a black and whiteoriginal. Color reproduction requires the reproduction of many differentcolors and shades. The multitude of colors is produced in conventionalprinting processes by the three subtractive primary colors, cyan,magenta and yellow. For high-quality reproduction a fourth ink, black,is also utilized. For large-volume reproduction of an original colorpattern, there is prepared a set of halftone printing plates, with eachcarrying a halftone image of one color component of the originalpattern. The original pattern is reproduced by overprinting with eachprinting plate so that the three printing inks visually combine toproduce the correct colors.

The printing plates needed for color printing may be derived by scanningthe original pattern in an electronic color scanner machine as set forthin U.S. Pat. No. 3,622,690. The color scanner typically scans theoriginal pattern with light and measures the tones or color in thepattern by filtering the scanned signal with red, blue, and green colorfilters. The amplitudes of the filtered signals indicate the colorcontent of the original pattern. Since the color printing inks are notspectrally perfect and hence do not correspond exactly to the threesubtractive colors, the filtered signals are corrected for thesedeficiences by means of color correction circuits in the color scanner.The color corrected signals are utilized to modulate the light emittedfrom a laser to produce continuous tone color separations of theoriginal pattern. The continuous tone color separations are thenscreened photographically and further processed to prepare the halftoneprinting plates. Alternately, screened color separations are directlyprovided without requiring a separate photographic screening step.

Other halftone techniques utilize variations of character generationschemes whereby various elements of a two-dimensional matrix are turnedon or off to create various dot patterns and characteristics. Alternatetechniques deflect a CRT beam or laser beam in such a manner as to drawdots of various shapes and characteristics. The dots are then repeatedspatially to generate a halftone grid.

Prior art systems may incorporate electronic schemes which generate ahorizontal or vertical line halftone, the scheme utilizing a pulse widthmodulation technique. In particular, a reference signal, which may betriangular, sine, cosine, waveform, depending upon the desired amplitudeto pulse width conversion characteristics, is applied to a voltagecomparator which compares the reference signal with a signalrepresenting the tonal values of a scanned original. The comparatoroutput may be coupled, for example, to a cathode ray tube to controlspot size. The aforementioned U.S. Pat. No. 3,465,199 is an example ofsuch a system. U.S. Pat. No. 3,916,096 discloses a technique forconstructing a two-dimension halftone by using an electronic linescreening technique. In particular, a single reference signal isamplified in separate, parallel channels. The amplified outputs arecompared with a video signal in separate comparators, the screened videooutput being switched between comparator outputs thereby providing twodifferent dot line widths. The system described in this patent provides,in essence, a line halftone and not a continuously varyingtwo-dimensional spot. Although the screened video output pattern may berecorded on a reproduction device, limited control of the shape of thedots generated and the angular relationship of the generated dots inrelation to the scanning direction is provided.

The line halftone techniques set forth hereinabove for convertingcontinuous tone originals into halftones do not provide the reproductiondetails required in many applications. Further, it would be desirable toadapt electronic halftone techniques to directly reproduce, or copy, ablack and white or color original document either locally or at a remotelocation. Although black and white, and recently, color copiers, arecommercially available, the techniques utilized therein providereproductions which although satisfactory for most purposes, are limitedin some respects. In particular, reproduction of continuous tone, blackand white and color originals have not provided the details required incertain applications.

It would be desirable, therefore, if two-dimensional electronic halftonetechniques can be provided for black and white and color copyingprocesses which allow the shape and characteristics of the halftone dotsto be easily controlled, provides for electronic screen simulation andangular rotation thereof to reduce Moire pattern effects, is economicaland reliable and which provides a reproduction or copy whose tonalcharacteristics are a substantial replica of that in the original.

SUMMARY OF THE PRESENT INVENTION

The present invention provides method and apparatus for scanning adocument original, either black and white or color, and reproducing acorresponding halftone reproduction thereof either locally or at aremote location. A halftone signal is generated by pulse widthmodulating, or comparing the scanned or video signal with a periodicsignal having two frequencies and phases to create a two-dimensional,continuously varying dot pattern output which is a function of thefrequency and phase of the two combined modulating signals. The halftonereproduction generated has variable dot configurations that arecontrollable to enable both rotation of the dot pattern (screen angle)and geometric modifications of the dot pattern. If the document originalis in color, light of three different colors is caused to scan thedocument, each resultant video signal being processed in a manner as setforth hereinabove. In a preferred embodiment, the different screenangles are utilized and each color comprises the reproduction.

It is an object of the present invention to provide method and apparatusfor scanning either a black and white or color original document andreproducing a corresponding black and white or color halftone imageeither locally or at a remote location.

It is a further object of the present invention to provide an electronichalftone generator which generates a halftone dot matrix whichcorresponds to a continuous tone original, the dots varying in size andshape in accordance with a predetermined periodic function.

It is still a further object of the present invention to provide anelectronic halftone generator which utilizes a screening function whichis periodic in time with dual frequencies and phases, the screeningfunction allowing the characteristics of the two-dimensional dot gridwhich comprises the halftone pattern to be varied and the screen anglethereof to be rotated, the latter to avoid Moire pattern problemsinherent in using multiple screens.

It is a further object of the present invention to provide atwo-dimensional grid of halftone dots wherein the dot characteristicscan be varied by varying a screening function and wherein the halftonegrid can be rotated relative to the input or output scanning direction.

It is still an object of the present invention to provide an electronichalftone generator for reproduction and/or display purposes which isoperative in real time and requires no data storage.

It is an object of the present invention to provide method and apparatusfor displaying an electrical signal representing an image or videoinformation as a predetermined halftone grid pattern on a displaydevice.

It is a further object of the present invention to provide method andapparatus for scanning a document original, either black and white orcolor, and reproducing a corresponding halftone reproduction thereofeither locally or at a remote location. A halftone signal is generatedby pulse width modulating, or comparing, the scanned or video signalwith a periodic signal having two frequencies and phases to create a dotpattern output which is a function of the frequency and phase of the twocombined modulating signals. The halftone reproduction generated hasvariable dot configurations that are controllable to enable bothrotation of the dot pattern (screen angle) and geometric modificationsof the dot pattern. If the document original is in color, light of threedifferent colors is caused to scan the document, each resultant videosignal being processed in a manner as set forth hereinabove. In apreferred embodiment, the different scan angles are utilized for eachcolor that comprises the reproduction.

DESCRIPTION OF THE DRAWING

For a better understanding of the invention as well as other objects andfurther features thereof, reference is made to the following descriptionwhich is to be read in conjunction with the accompanying drawingswherein:

FIG. 1 illustrates a pulse width modulator utilized in the prior art;

FIG. 2 illustrates the application of pulse width modulation techniquesto line halftone generation;

FIG. 3 is a line halftone time phase diagram;

FIG. 4 is a simplified diagram illustrating the basic concept of thepresent invention;

FIG. 5 illustrates characteristic dot shapes for a particular screeningfunction;

FIG. 6 illustrates alternate implementations of the electronic halftonegenerator of the present invention;

FIG. 7 is a simplified schematic of the electronic halftone generator ofthe present invention;

FIGS. 8-10 show a schematic diagram of one embodiment of the presentinvention for a fixed screen angle;

FIG. 11(a) shows a dot matrix for a 45° standard screen and FIG. 11(b)shows a dot matrix for a 45° elliptical screen; and

FIG. 12 is a block diagram illustrating a halftone color reproductionsystem which utilizes the electronic halftone generator of the presentinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In order to illustrate the novel features of the present invention, abrief description of prior art electronic halftone dot generatortechniques will be briefly set forth.

The majority of approaches use variations of character generationschemes whereby various elements of a two-dimensional matrix are turnedon or off to create various dot patterns and characteristics. Thepatterns are then repeated to construct the halftone dot matrix. Othertechniques deflect a CRT beam or laser beam in such a manner as to drawdots of various shapes and characteristics. The dots are then repeatedspatially to generate the halftone dot matrix (grid).

The technique which is similar in some respects to the technique of thepresent invention is the application of pulse width modulationtechniques to generate a horizontal or vertical line halftone. The pulsewidth modulation (PWM) technique is illustrated schematically in FIG. 1.The reference signal is a periodic function of time with frequencyf_(c). The reference waveform can be, for example, triangular, sine orcosine, in shape depending upon the desired amplitude to pulse widthconversion characteristics. The frequency (clock) f_(c) is generally afactor of two or more greater than the high frequency cutoff of thevideo signal to satisfy information and sampling theory criteria. Thedynamic range (D.R.) of a system using a dot matrix halftone (dynamicrange being defined as the ratio between maximum reflectivity [orbrightness] to minimum reflectivity [or brightness] in the outputexcluding the complete absence of dots or lines) is given by the ratioof the clock period T_(p) (1/f_(c)) to the minimum pulse duration(t_(p)) that can be tolerated and/or produced at the output,

    D.R.=(T.sub.p /t.sub.p)=(1/f.sub.c t.sub.p).

The application of PWM to line halftone is schematically illustrated inFIG. 2 and is basically the same. The reference frequency is

    f.sub.c =f.sub.l v

where f_(l) is the line halftone spatial frequency and v is the scanvelocity in the appropriate direction (X or Y). The reference signalphase φ is adjusted to obtain proper alignment of the halftone linepattern. In general, the reference frequency is less than the highfrequency cutoff of the video (particularly for line halftones orientedsuch that the lines are parallel to the X (high velocity) scandirection). The line halftone time phase diagram using a triangularreference waveform is shown in FIG. 3. A light output is produced whenthe video input is greater than the reference signal for positiveprinting or display. This technique enables high frequency and highcontrast video to be retained as shown in A in FIG. 3. The dynamic rangeis given by the ratio of the line spacing (l) to the minimumreproducible line width (d), i.e.,

    D.R.=(l/d)=(1/f.sub.l d)

The limited dynamic range and the general limitations of vertical orhorizontal line halftone orientation is characteristic of theapplication of PWM prior art to halftone generation. As will be setforth hereinafter, the present invention increases the dynamic range ofhalftone systems while providing additional advantages such as screenrotation and dot shape selection using electronic techniques.

FIG. 4 illustrates the basic concept of the present invention. F(v) is afunction of the input video and S(f₁, f₂, φ₁, φ₂, t) is the screeningfunction which, as will be set forth in detail hereinafter, provides forscreen rotation and dot shape selection. The screening function isperiodic in time with dual frequencies and phases. It is the dualfrequency nature of the screening function which provides a significantimprovement in capabilities over the line halftone technique describedhereinabove. The normalized output of comparator 8 is defined as

    V.sub.o =1, F>S; V.sub.o =0, F<s

for direct output and

    V.sub.o =1, F>S; V.sub.o =0, F<S

for complimentary output. The direct output or complimentary output isthe halftone signal to be used for reproduction and/or display with anoutput of 1 defined as white and an output of 0 defined as black. In thepreferred embodiment the input and output scan techniques and devicesare of a rectilinear X-Y nature.

However, this does not preclude the use of alternate scanning techniquessuch as circular, spiral, etc. in the present invention. In X-Y scanningapplications the frequencies are defined as

    f.sub.1 ≡f.sub.x =v.sub.x f.sub.d ; f.sub.2 ≡f.sub.y =v.sub.y f.sub.d

where v_(x) and v_(y) are the scan velocities in inches/sec in the X andY directions respectively and f_(d) is the spatial dot frequency desiredin dots per unit length, i.e. dots/inch. The phase terms are defined by

    φ.sub.1 =φ.sub.x, φ.sub.2 =φ.sub.y

and provide proper synchronization of the halftone screen with thescanning devices. The phase terms can be dropped from further discussionsince the phase (absolute) defines starting point (where scanning spotsstart from edge of the reproducing medium) determined, for example, by ascan start signal, without the loss of generality as long as therelative phase is maintained.

The condition for which the comparator switches states is given by

    S(f.sub.x,f.sub.y,t)=F(v)

and represents the locus of points defining the halftone dot shape. Inparticular, at the scanning point where S=F, the output V_(o) changesfrom white to black or black to white. A series of scan lines, typically7 or 8, builds up the actual dot. The screening function S determinescharacteristic dot shapes for uniform grey value inputs (F constant)whereas the video function F determines the grey value displayed and/orreproduced for various grey value inputs. The following are examples ofhalftone patterns produced for various screening functions:

(1) A screening function which is the linear sum of two triangular waveswith frequencies f_(x) and f_(y), i.e.,

    S(f.sub.x,f.sub.y,t)=T.sub.1 (f.sub.x t)+T.sub.2 (f.sub.y t)

will generate a halftone parallel to the X and Y scan directions havingdots which are diamond shape for constant grey value input (a videosignal of uniform intensity during the active portion of the scanningsystem and represents a uniform density or reflectivity ortransmissivity of the scanned original). The tone reproduction curve(density in/density out) will have a gamma=2 for

    F(v)=cv+d

and a gamma=1 for

    F(v)=√cv+d

where c and d are arbitrary constants to match input and output whiteand black and characterize the electronic signal representative of thescanned original document.

(2) A screening function given by

    S(f.sub.x,f.sub.y,t)=T.sub.1.sup.2 (f.sub.x t)+T.sub.2.sup.2 (f.sub.y t)

will produce a halftone grid with characteristic dot shapes which arecircles. The circles will merge for certain values of F(v) and the tonereproduction curve (TRC) is in general non-linear. However, anappropriate choice of F(v) can linearize the TRC.

From these examples it can be seen that appropriate choice of thescreening function, S, and video function, F, can provide a wide varietyof dot shape characteristics and TRC's.

The most useful screening function is a combination of sines and/orcosines waveforms as the dot shape characteristics will match thosepresently achieved in the photo-lithographic industry using opticalcontact halftone screens. The screening function

    a cos 2πf.sub.x t+b cos 2πf.sub.y t=F(v)             (1)

will produce the dot shapes shown in FIG. 5 for various values ofK=(F(v)/a) and a≡b. For a≠b the dot shape will expand or compress in onedirection, without changing the dot frequency in either direction,thereby duplicating the characteristics of "elliptical" screens in thephotolithographic industry. "Elliptical" screens have the effect ofreducing visual contouring effects when the points of adjacent dots justtouch. The constant "a" can represent the voltage or current gain in theelectronics and the constant "b" can represent the D.C. offset voltageor current. The magnitude of these constants are determined at the inputto the comparator by the peak-to-peak voltage and D.C. offset of thehalftone reference signal and the halftone dot size desired in thehighlight and shadow regions in the reproduction and/or display of theoriginal document.

The above screen function produces a halftone grid defined as a 0°screen since the grid is parallel to the X or Y scanning directions.Screen angles other than 0° can be produced with the screening function

    S(f.sub.x,f.sub.y,t)=a cos 2π(f.sub.x cosθ+f.sub.y sinθ)t+b cos 2π(f.sub.x sinθ-f.sub.y cosθ)t         (1a)

where θ is the desired screen angle. For a=b, a standard screen (forexample, highlight and shadow data will be circular in shape) isproduced and for a≠b an "elliptical" screen is produced where thechaining direction, i.e., direction in which the adjacent dots firsttouch at midpoint grey, is either parallel or perpendicular to thescreening direction θ. If θ is ±45° the above screening functionsimplifies to

    S=a cos √2π(f.sub.x +f.sub.y)t+b cos √2π(f.sub.x -f.sub.y)t= 2a cos √2πf.sub.x t cos √2πf.sub.y t+(b-a) sin √2πf.sub.x t sin √2πf.sub.y t     (2)

for elliptical screens.

This simplifies further for a standard screen (a≡b) to

    S=2a cos √2πf.sub.x t cos √2πf.sub.y t (3)

and differs from 0° screens by a reduction in frequency of √2, a factorof 2 increase in gain, and multiplying the references instead of adding.It should be noted that screen rotation can be achieved with equation(2) as a starting point instead of equation (1), thereby reducing thefrequency range required of the references (f_(x) cosθ, f_(x) sinθ,f_(y) cosθ, f_(y) sinθ) for certain ranges of θ.

In general, the video function F(v) is selected to be a monotonicallyincreasing or decreasing function of the input video. A monotonicallyincreasing function is defined as a function of a variable whichincreases as the variable increases and decreases as the variabledecreases without discontinuities within the variable range i.e. forf=f(x), df/dx>0 and continuous for x₁ ≦x≦x₂ where x₁ and x₂ define therange of monotonicity. A monotonically decreasing function is defined asa function of a variable which decreases as the variable increaseswithout discontinuities over the variable range, i.e., f=f(x), (df/dx)<0and continuous for x₁ <x<x₂ where x₁ and x₂ define the range ofmonotonicity. For example, the function f=x² is a monotonicallyincreasing function of x for all x greater than zero and is amonotonically decreasing function of x for all x less than zero; thefunction f=x³ is a monotonically increasing function of x for all x. Ifg(v) is defined as a monotonically increasing function of video, thenF(v) can be represented as

    c(g(v)+d) or (c/(g(v)+d))

where c and d are the constants as set forth hereinabove. The thresholdconditions can then take the forms

    ______________________________________                                                                  Case                                                ______________________________________                                        s(f.sub.x,f.sub.y,t) = c(g(v) + d)                                                                        I                                                 S - c(g(v) + d) = 0         II                                                 ##STR1##                   III                                                ##STR2##                   IV                                                 ##STR3##                   V                                                 (g(v) + d)S = c             VI                                                ______________________________________                                    

The implementation of these conditions are shown in simplified form inFIG. 6. The outputs will be positive or negative depending upon theCase. The complimentary outputs can be used or obtained if desired. Thegain and offset need not be applied to g(v) but can instead be appliedto S(f_(x),f_(y),t) if desired without loss of generality. An electronicgain adjustment sets the constant "c" and the addition or subtraction ofa D.C. offset voltage or current sets the constant "d". As set forthhereinabove, the actual settings are determined by the desired halftonecharacteristics in the reproduction and/or display (highlight and shadowdot sizes). Case's I, II, IV and V are sometimes referred to as additivescreening. Case III is divisional screening and Case VI ismultiplicative screening. Case VI is analogous to photolithographictechniques where g(v) is the negative or positive to be halftoned, S isthe halftone screen, and c and d are analogous to bump and flashexposures ("bump and flash" are terms utilized to define the proceduresused in the photolithography industry to adjust the halftonecharacteristics, i.e. highlight and shadow dot sizes). All theaforementioned cases are equivalent as far as dot shape characteristicsare concerned and differ only in TRC corrections required in g(v) toobtain the desired result.

For purposes of illustrating the present invention, the Case Ielectronic implementation will be described hereinbelow. The simplifiedschematic diagram of the halftone generation for Case I is shown in FIG.7 and incorporates both a 0° reference angle (implementation of equation(1)) and 45° reference angle (implementation of equation (2)) for screenangle rotation. The functions cos f₁ t, cos f₂ t, sin f₁ t and sin f₂ tmay be generated by phase locked oscillators, digital synthesizers or anarray of PROMS approximately programmed to generate the desiredfunctions. Analog multipliers 10 and 12 generate 45° referencedwaveforms. Multiplier 10 generates a standard screen by multiplying cosf₁ t and cos f₂ t and multiplier 12 provides ellipticity correction forthe 45° screen. Ganged switches S₁, S₂ and S₃ determine the ellipticitychaining direction whereas ganged potentiometers 14 and 16 and variableresistors 18 and 20, respectively, adjust the amplitude of the screenfunctions referred to 0° for the amount of ellipticity. Resistor 18 istrimmed to equal the resistance of potentiometer 14 as determined by thesetting of its adjustable tap 22 and resistor 20 is trimmed to equal theresistance of potentiometer 16 as determined by the setting of itsadjustable tap 24. Adjustable tap 26 of potentiometer 28 adjusts theamount of dot ellipticity for screen functions referred to 45°. SwitchS₄ selects 0° reference or 45° reference for appropriate screen angles.Summing amplifier 30 assembles the screen function and gain and offsetdevice 32 adjusts the video function for appropriate maximum and minimumdensities in the reproduced and/or displayed output, the adjusted videofunction being compared with the screening function in comparator 34.Adjustable taps 22 and 24 adjust the constants a and b in equations (1)and (1a) in such a way that a+b equals a constant such that the voltagevalues of white and black (0% and 100% relative dot area) as defined bythe screening function are independent of the setting of taps 22 and 24.Tap 26 adjusts (b-a) in Equation (2), with "a" predetermined prior tothe halftone generator, in such a way that voltage values of white andblack (0% and 100% relative dot area) as defined by the screeningfunction are independent of the setting of tap 26. The chainingdirection switches S₁ and S₂ determine the conditions b≧a or b≦a whichestablishes the direction of "chaining", i.e., the direction in whichthe halftone dots change size most rapidly with changes in video signal.The switch S₃ selects (b-a)≧0 or (b-a)≦0, i.e., b≧a or b≦a to establishthe chaining direction.

The combination of multiplier 12, inverter 13, switch S₃ and tap 26 ofpotentiometer 28 determine±(b-a) sin f₁ t sin f₂ t which is the secondterm in Equation (2). In particular multiplier 12 generates the productof sin f₁ t and sin f₂ t, the inverter changes the sign of the product,i.e., plus to minus or vice versa, S₃ selects the appropriate sign forthe chaining direction desired, and 26 and 28 determine the magnitude of(b-a). S₄ in the position as shown in FIG. 7 selects the θ=0° case andall rotation angles referred to 0°, i.e. θ=23° to 45°. When S₄ is placedin the alternate position, the θ=45° and screen angles referred to 45°,i.e., θ=0° to 22° are selected. By having the 23° to 45° angles referredto 0° and the 0° to 22° angles referred to 45°, the inherent problems ofgenerating a sine function of a small angle, a very small value, andmultiplying it with other values to obtain f₁ and f₂ can be obviated.The actual screen angles are determined by proper generation of theappropriate reference frequencies f₁ and f₂ such that ##EQU1## Referringto Equation (1a) ##EQU2## and referring to Equation (2) ##EQU3##Equation (3) gives: ##EQU4##

It should be noted that for the elliptical case, interchanging f₁ and f₂and the left side of the above equations has the effect of interchangingthe chaining direction, i.e., the switch positions of S₁, S₂, and S₃ inFIG. 7 are interchanged for a given chaining direction. The rotationangles that can be achieved are not limited to the above values but canbe any angles. The above angle ranges θ=0° to 22° and θ=23° to 45° werechosen to ease the dynamic range requirements on f₁ and f₂ frequencies.The rotation angles are not limited to integer values as non-integerrotation angles can be implemented, e.g., θ=22.333° . . .

FIGS. 8, 9 and 10 show a particular implementation of Case II shown inFIG. 6 for a screen angle of 45°. In this case, f₁ =(fx/√2) and f₂=(fy/√2). Assuming a desired spatial dot frequency of 100 dots per inchand a scan velocity 2.8×10⁴ inches per second in the horizontaldirection, fx=2.8 MHz and f₁ =1.98 MHz. For a scan velocity of 5.32inches per second in the vertical direction and a dot frequency of 100dots per inch, fy=532 Hz and f₂ =376 Hz.

Typical dot frequencies are in the range from about 65 dots/inch toabout 150 dots/inch (horizontal and vertical), typical values of fx arein the range of about 1 MHz to about 6 MHz and typical values of fy arein the range of about 250 Hz to about 8 KHz (preferred ratio of fx to fyis 10⁴).

For a standard screen, the screening function is given by equation (3)hereinabove.

The cos f₁ t signal 50 is applied to terminal 52 of balanced modulator54 via function synthesizer 49, the modulator functioning as a fourquadrant multiplier. The cos f₂ t signal is applied to terminal 58 ofmodulator 54 via function synthesizer 57. The output 60 appearing atterminal 62, the screen function desired, is a suppressed carrier doublesideband signal which is coupled to a comparator for comparison with theinput electrical signal. The output of the comparator may be applied toa modulator which provides an information containing optical signalwhich is coupled to an appropriate reproduction device. The device whichsynthesizes the f₁ and f₂ functions is synchronized by a start of scansignal (on the x-direction) from the reproduction device to initiate thewaveform generation at the same time the scanning device starts to scaneach line. The function synthesizer is also responsive to the number oftimes an original is being scanned such that, in a color reproductionmode, the screen angle can be varied for each scan of the original. Forreproductions of a black and white original, the screen angle ismaintained constant, preferably at 45°.

The function synthesizer, in the preferred mode, generates sine/cosinewaveforms of variable frequency determined by the values of the screenangles as applied to the equations set forth hereinabove. A programmablewaveform generator, such as the XR-205 Monolithic Waveform Generator,manufactured by Exar Integrated Systems, Inc., Sunnyvale, Calif., istypical of a precision function synthesizer which can provide a variablefrequency signal output which is dependent upon a controllable input.Alternately, two separate wave generators can be provided to generatethe required two separate frequencies, the frequencies desired beingentered into the waveform (frequency) generators by, for example,external switches. For color scanning, a sequence selector can beprovided to automatically select an appropriate output frequency fromthe waveform generator in accordance with the color being scanned(actually the selection is dependent on whether the original is beingscanned the first, second or third time as will be explainedhereinafter). Alternately, three pairs of waveform generators (sixtotal) could be provided for three different screen rotations in thecolor scanning mode, a switch driven off the reproduction device) beingprovided to allow for the proper pair selection.

In order to modify the circuit of FIG. 8 to produce a non-standardscreen (elliptical dots), the block diagram of FIG. 9 is utilized. Thesignals 50 and 56 are applied to balanced modulators 72 and 74, to thelatter via 90 degree phase shifters 76 and 78, via function synthesizers49 and 57. The outputs 81 and 83 from the modulators 72 and 74,respectively, are summed in summer 80 to produce the screening function85 as set forth in equation (2) hereinabove. The values for constants"a" and "b" can be electronically controlled in the modulators orcircuitry provided with the comparator as shown in FIG. 10. The degreeof ellipticity depends on the ratio of the output signals from eachmodulator (or the difference in peak-to-peak amplitudes of the output ofeach modulator) 72 and 74. The output signal 85 from summer 80 iselliptical, 45° screening function desired.

FIG. 10 illustrates the comparator schematic circuit. The electricalanalog input signal, such as a video signal, is applied to inputterminal 90, the gain thereof being controlled by potentiometer 92. Theinput signal is applied to the base of NPN transistor 94 via resistor96. The screening function is applied to terminal 98 and to the base oftransistor 94 via resistor 100. Potentiometer 102 and the 5 volt sourceapplies offset currents to the transistor base via resistors 104 and 112respectively. The currents appearing at the transistor base are summedand converted to a voltage by a summer amplifier circuit comprisingtransistor 94, load resistor 108 and feedback resistor 110 connected asshown. The summed voltage signal at the collector of transistor 94 iscoupled to the non-inverting input of comparator 114. A thresholdcircuit, comprising a resistive divider circuit (resistors 116 and 118),the voltage source and capacitor 120 (acting as a filter) provides athreshold signal to the inverting lead of comparator 114. When thesignal on the non-inverting input is greater than the signal on theinverting input, comparator 114 generates a variable width positivepulse (sliced video) at terminal 122 which varies from 0 volts to +3volts in amplitude. The signal at terminal 122 is then applied to amodulator, as shown in FIG. 12, the modulator controlling the on-offtimes of the laser beam to provide the desired halftone reproductions.

FIG. 11(a) illustrates the generation of a portion of a 45° standardscreen at the 50 percent gray point (corresponding to the dot K=0.5 inFIG. 5), the dots in the standard screen being symmetrical to adjacentdots both in the screening direction and orthogonal thereto. Forpurposes of illustration, the pattern generated is initiated at startpoint 140 which is synchronized with the scanning reproduction deviceutilized as described hereinafter with reference to FIG. 12. Referencearrow 141 indicates the direction of the x-scan and reference arrow 143indicates the direction of the y-scan.

The dots 144, 148, 150, 154, 160 and 164 constructed for the 50 percentgray point illustrated are assumed for illustrative purposes, tocomprise four scan lines, or rows, each. These dots are formed withindiamond shaped halftone cells 142, 146, 152, 156, 158 and 162,respectively, each halftone cell being typically 10 mils on each side(for a 100 dot/inch screen frequency). The diamond shaped cell area (theoutline of which is shown in the Figure) corresponds to the dot shape(K=0.5) of FIG. 5. It should be noted that for a screen pattern whichrepresents full black, the dots shown would substantially fill itsassociated halftone cell and adjacent cells would be printed black (orin color for the color scanning mode). The 45° screen function causesthe grid matrix illustrated to be reproduced by an emitting beam, suchas a laser, coupled to a reproduction device such that a dot in cells144, 148, 150, 154, 160, 164 . . . is produced whereas no dot isconstructed in adjacent cells 142, 146, 152, 156, 158, 162 . . .Referring more particularly to the construction of dot 144 forillustrative purposes, the first write, or laser scan, produces dotportion a, the second scan produces dot portion b, the third scanproduces dot portion c and the fourth scan produces dot portion d (thedot portions generally overlap). The pattern shown corresponds tomidtone gray as those cells corresponding to the dots actuallyconstructed would be printed as completely black (or in color for thecolor copying mode). As can be seen in the Figure (and FIG. 11(b)described hereinbelow), the direction of the dot portions (a, b, c andd) in each scanline is the same, i.e. in the direction of scan indicatedby arrow 141. The alignment of the entire dots, which comprise all thedot portions (four in the example illustrated), is variable andcontrolled by the screening function utilized.

Although not shown, other dot configurations could also be constructed.For example, a circular highlight dot could be constructed byappropriate selection of the screening function (K=0.1, FIG. 5).

FIG. 11(b) illustrates the generation of a portion of a 45° non-standard(elliptical) screen grid using the circuit configuration of FIGS. 9 and10. The dots generated in this grid by definition, are non-symmetricalto adjacent dots both in the screening direction and orthogonal thereto.For grays corresponding to highlight and shadow areas, the dotsconstructed actually look like ellipses, hence the name for thenon-standard screen. In the mid-tone range, the cell which defines themaximum dot area is not entirely printed as black (or in color for thecolor copying mode). For increased levels of gray, the dots shown inFIG. 11(b) will continue to increase in area until adjacent dots merge.

The scanning operation is initiated at point 170, the x-direction ofscan being indicated by reference arrow 171 and the y-scan directionbeing indicated by reference arrow 173. The dots 174, 178, 180, 184, 190and 194 generated are formed within a plurality of respective halftonecells 172, 176, 182, 186, 188 and 192 of a size, for example, as setforth hereinabove with reference to FIG. 11(a). As can be seen, the dotmatrix forms a 45° angle to the x-direction of scan. Referring tohalftone cell 172 for illustrative purposes, the dot 174 generatedcomprises portions a, b, c, and d which may or may not overlap. Theportions a, b, c, d of dot 174 may be considered to form the outline ofan ellipse, the chaining direction of which is parallel to the screeningdirection. The dots in halftone cells 172, 176, 182, 186, 188 and 129are similarly constructed to form the mid-tone pattern illustrated. Inthis situation, only two corners of a constructed dot are touchingadjacent dots. For example, the corners of dot 184 touch the corners ofdots 178 and 190 but no portion of dot 184 is touching dots 174 and 194.Other non-standard screens can be provided to provide alternate dotconfigurations using the teachings of the present invention.

Referring now to FIG. 12, a block diagram illustrating a color copyingsystem in which the present invention may be utilized is shown. Itshould be noted that the present invention may be utilized in a blackand white copying system wherein a laser having a single outputwavelength may be utilized to scan an original and print a reproductionthereof on a laser sensitive medium. In this case, the screening angleis maintained constant for each line scan. An original document 210 ispositioned on a rotating member 212 which, in the embodiment shown, isdrum shaped. The document 210 is secured to the drum 212 by suitablemeans and the drum is caused to rotate in the direction of arrow 214.Original document 210 may be black and white or in color. The discussionset forth hereinafter will be directed to the scanning of a colordocument 210. Since the concept of the present invention is directed toscanning the original document 210 and reproducing a copy either setforth hereinabove with reference to FIG. 11(a). As can be seen, the dotmatrix forms a 45° angle to the x-direction of scan. Referring to cell174 for illustrative purposes, the elliptical dot generated comprisesportions a, b, c, and d which may or may not overlap. The portions a, b,c, d of dot 174 forms the outline of an ellipse, the chaining directionof which is parallel to the screening direction. The dots in alternatecells 178, 180, 184, 190 and 194 are similarly constructed to form themid-tone pattern illustrated. In this situation, only two corners of aconstructed dot are touching adjacent dots. For example, the corners ofdot 184 touch the corners of dots 178 and 190 but no portion of dot 184is touching dots 174 and 194. Other non-standard screens can be providedto provide alternate dot configurations using the teachings of thepresent invention.

Referring now to FIG. 12, a block diagram illustrating a color copyingsystem in which the present invention may be utilized is shown. Itshould be noted that the present invention may be utilized in a blackand white copying system wherein a laser having a single outputwavelength may be utilized to scan an original and print a reproductionthereof on a laser sensitive medium. In this case, the screening angleis maintained constant for each line scan. An original document 210 ispositioned on a rotating member 212 which, in the embodiment shown, isdrum shaped. The document 210 is secured to the drum 212 by suitablemeans and drum is caused to rotate in the direction of arrow 214.Original document 210 may be black and white or in color. The discussionset forth hereinafter will be directed to the scanning of a colordocument 210. Since the concept of the present invention is directed toscanning the original document 210 and reproducing a copy either locallyor at a remote location, document 210 is scanned to generate appropriateelectrical (video) signals which represent the tonal (color) informationon document 210. In particular, read lasers 216, 218 and 220 areprovided, laser 216 comprising a helium-neon laser for generating redlight, laser 218 comprising a helium-cadmium metal vapor laser forgenerating blue light and laser 220 comprising an argon-ion laser forgenerating green light. It should be noted that a properly excitedhelium-cadmium laser can provide light having wavelengths correspondingto both blue and green and therefore a single laser can be utilized inplace of lasers 218 and 220. The light beam 222 from laser 216 isdirected to a fully reflecting mirror 224 which directs the beam tomirror 226 which is transmissive thereto. Mirror 226 also reflects beam228 generated by laser 218 so that resulting beam 230 comprises both redand blue light. The beam of light 232 generated by laser 220 is directedto mirror 234 which transmits beam 230 and reflects beam 232. Theresulting beam 236 from mirror 234 combines the red, blue and greenwavelengths generated by lasers 216, 218 and 220, respectively, and isincident on mirror 238. Beam 236, which is essentially white light, isdirected via mirror 238 into input scanner 240 which may comprise arotating multifaceted polygon. The scanning light from scanner 240 isdirected to the document 210 via cylindrical lens 242 which has itsplane of no power in the direction of scan. The light reflected fromdocument 40 is collected by light pipe 244 which in turn directs thecollected light to a detector 246 which comprises sections 246a, 246band 246c which is responsive to the red, blue and green light,respectively, reflected from color document 210. The detected output iscoupled to a color correction computer 248 for appropriate processing.Color correction computers are well known in the prior art (see U.S.Pat. No. 3,622,690, for example) and correct for the deficiencies in thedeveloper powder (toner) and provides consecutively a plurality ofelectronic color separation signals therefrom corresponding to thecolors yellow, magenta and cyan. As will be explained hereinafter withrespect to the printer utilized, original document 210 is scanned threetimes to provide video signals corresponding to the three primarycolors, color correction computer 248 thereafter being operated in acorresponding sequence to provide color corrections for the yellow,magenta and cyan developer powder. The color correction generated bycolor correction computer 248 is applied to the halftone electronicgenerator 250 of the present invention via lead 252. A start of scandetector 254 is provided adjacent document 210 to provide the requiredsynchronizing signal to the electronic generator 250 via lead 256. Thefunction synthesizers, utilized for generating sine/cosine waveforms,are gated by the start of scan signal to insure the same phase (i.e.phase equal to zero degrees in the x-scan direction) for each scan line.A shaft encoder 260 generates a pulse for each revolution of the drum,the pulse train generated thereby being coupled to counter 262 whichcounts three pulses and is reset thereafter. For color reproduction, thedocument 210 is scanned three times, once each to scan for the red,green and blue colors which comprise the document information. It shouldbe noted that a fourth color, such as black, can be scanned andreproduced with an additional scan and screening function. Since it isdesired to provide a different screen angle for each scan (a singlescreen angle can be used for black and white reproductions) the firstpulse detected causes counter 262 to generate a signal on lead 264 whichis coupled to electronic halftone generator 250. The functionsynthesizer therein generates an appropriate screen function having afirst screen angle (relative to the x-direction of scan) therefrom. Thesecond pulse detected, corresponding to the second document scan, causescounter 262 to generate a signal on lead 264 which causes the functionsynthesizer to generate a screen function having a second screen angle,different from the first screen direction. The third pulse detected bycounter 262, corresponding to the third document scan, causes thefunction synthesizer to generate a screen function having a third screenangle, different from the first and second screen directions. Forexample, the first screen angle may be 0°, the second screen angle 22°and the third screen angle 45°. In this manner, an accurate colorhalftone reproduction of the original document 210 is produced by thereproduction device. In particular, the halftone signal is applied to anelectro-optic modulator 266 via lead 268 to produce halftone separationsof the document 210. The output beam from write laser 270 is alsoapplied to modulator 266 via mirror 272. As will be explained in moredetail hereinafter with reference to reproduction device, or printer274, it is preferred that write laser 270 generate red light such asthat generated by a helium-neon laser. The modulator 266 modulates laserbeam 276 in accordance with the amplitude of the electronic signalsderived from halftone generator 250. In general, when these signals arehigh, more light is passed by modulator 266 then when the signals arelow. Consequently, the light transmitted through the modulator 266 is afunction of the amplitude of the electronic signals on lead 268 andhence is a function of the density (color) of the tones on document 210.The light transmitted through the modultor 266 is applied to an outputscanner 278 which is similar to input scanner 240 and is in synchronism,therewith. The scanning light from output scanner 278 is focused bycylindrical lens 280 onto a photoconductive medium 280 formed onxerographic drum 284. The printer, generally labeled 274, in thepreferred mode comprises the system disclosed in U.S. Pat. No. 3,854,449modified to incorporate laser 270, modulator 266 and output scanner 278.The teachings of U.S. Pat. No. 3,854,449 necessary for the understandingof the invention are incorporated herein by reference. As set forthhereinabove, electronic halftone generator 250 provides the necessarysignals to produce the required halftone dot matrix on the output copy.The particular circuitry utilized allows various shaped dots to begenerated at variable screening angles to the scanning direction. Withreference to FIG. 12, the scanning, or x direction, is in the directionperpendicular to the plane of the figure.

In operation, the reading lasers 216, 218, and 220 are turned on and themonochromatic light beams therefrom are merged into a single scanningbeam 236 which is focused onto input scanner 240. The rotation ofscanner 240 causes the scanning beam, focused by lens 242 into a finespot, to scan the document 210. A number of scan lines are produced asdrum 212 rotates in the direction of arrow 214. Each scan line producesvarying amplitudes light signals due to the color content of thedocument 210 which light signals are transmitted and collected by lightpipe 214 and detected by detectors 246a-246c. Detector 246a extracts thered light in the transmitted light beam and converts it to a varyingelectronic signal. The blue light in the scanning beam is extracted bydetector 246b and the corresponding electronic signal is generated anddetector 246c detects the green light in the scanning beam and convertsit into an electronic signal. The color component signals from thedetectors 246a-246c are applied to the color correction computer 248 toproduce color corrected magenta, cyan and yellow output signals. Thesevarying signals are applied to the modulator 266 via electronicgenerator 250 laser beam 276 derived from laser 270 also being appliedthereto. Modulator 266 passes or inhibits the laser beam light inaccordance with the amplitude of the electronic signal derived from thehalftone generator 250. The output from modulator 266 is focused ontothe xerographic drum 284 to expose photoconductor 282, the image beingdeveloped as set forth in U.S. Pat. No. 3,854,449. Since the modulatedlight is a replica of the corresponding color component in the originalpattern formed on document 210, the hard copy output produced from theimage on the drum 284 produces a halftone replica of the color tones indocument 210.

Since the developing process in printer 274 requires three scanningcycles, document 210 is scanned three times by input scanner 240, outputscanner 278 similarly scanning drum 284 three times in sychronism withthe scanning of document 210.

Although the present invention has been described with reference toanalog device implementations, the devices could be implementeddigitally.

The invention described hereinabove has great versatility and manyadvantages over the prior art in producing electronic halftones forreproduction and/or display purposes. It provides a two dimensional gridof halftone dots where the dot characteristics can be altered throughappropriate choice of screening function. The dot area is modulated bythe video function thereby providing a greater dynamic range than linehalftone techniques are capable of. With appropriate choice of screeningfrequencies and phases the halftone grid can be rotated relative to theinput and/or output scan directions and with use of appropriate phaseand/or frequency locking techniques the halftone grid pattern can becompensated for scan irregularities. Coordinate transformationstechniques may be provided to allow the present invention (whichproduces rectilinear halftone grids) to be produced with spiral,circular, etc. input/out scan devices. Paralleling many of thesecircuits with appropriate time delay of the same screening function willallow the use of a different number of output channels than inputchannels for application to multiple channel scanning devices. The videofunction is not band limited by the screening function and outputresolution for high contrast is not appreciably degraded. The output isbinary and need not have any greater bandwidth than the input videofunction, thereby providing data compression for video format signals.The aforementioned advantages are accomplished in real time without anystorage requirements.

As set forth hereinabove, the dynamic range of the line halftonetechnique is

    D.R.=(1/f.sub.l w)

where f_(l) is the line halftone frequency in lines per unit length andw is the minimum reproducible line width. The invention described hereinprovides a dynamic range given by

    D.R.=K(1/f.sub.d d.sub.s).sup.2

where f_(d) is the dot frequency in dots per unit length, d_(s) is thediameter of the smallest reproducible dot, and K is a geometric areafactor depending upon dot shape, K being 4/π for a circular dot. Ingeneral, the output scanner determines w or d_(s) and for w=d_(s), f_(l)=f_(d), the dynamic range of the electronic halftone generator is thesquare of the dynamic range for line halftone, e.g., a line halftonecapability of 8:1 will increase to 64:1 for dot halftone with the sameoutput scan limitations. This represents a considerable improvement inperformance.

The dual frequency and phase nature of the screening function allows forcoordinate manipulation using frequency and/or phase modulationtechniques. For example, proper choice of frequency and phase canproduce a rotated halftone grid relative to an X-Y scanner. Withappropriate frequency and/or phase modulation, coordinate transformationand stabilization can be achieved. For example, a rectilinear halftonegrid can be produced with a spiral scan output by setting

    f.sub.1 =v.sub.r f.sub.d cos wt

    f.sub.2 =v.sub.r f.sub.c sin wt

where v_(r) is radial scan velocity and w is the angular scan velocity.

If the scan velocities have irregularities due to mechanical constraintsor other causes which can be sensed then frequency and phase locktechniques can be applied to f₁ and f₂ to stabilize the halftone gridpattern.

In devices having input/output scanners of a multiple channel nature,the electronic halftone generator can be incorporated in each channel.The screening function is applied to each channel with an appropriatetime delay between channels thereby registering the reference halftonegrid.

Partial dots refers to the capability of modulating dot area within onehalftone grid cell in conjunction with a rapidly changing density inputin the video signal. The screening function allows a dot to change fromblack to white for example, in the middle of constructing the dot. Thefact that the electronic halftone generator technique does notfundamentally limit the video function bandwidth guarantees partial dotcapability.

The present technique inherently provides a data compression feature. Inparticular, the video function has a bandwidth of Δf and an analogdynamic range of D. If the video functions were converted to digitalformat, the bit rate, B, would be at least

    B=2 fΔlog.sub.2 D

The output of the electronic halftone generator is binary in nature witha minimum bandwidth of Δf and represents a bit rate of

    B=2Δf

This would be a data compression factor of log₂ D except for the factthat the output pulses are duration modulated. However, dynamic rangeconsiderations yield a net compression factor, C_(d) of

    C.sub.d =(log.sub.2 D/2)

for digitally converted halftone output. Further data compression may beobtained through conventional techniques. In special applications whereclocked bits are not required the full compression factor

    C.sub.d =log.sub.2 D

can be realized.

In summary, the electronic halftone generator of the present inventionconverts electronic signals in video format to binary output halftonesignals. Input devices providing video format signals can be TVscanners, laser scanners, flying spot scanners, video tape, computerconstructed imagery, facsimile, etc. The output of the generator, beingelectronic in nature, can be used with output devices incorporating anynumber of marking and/or display technologies. Output scanners can be,for example, CRT, lasers, flying spot, LED and electronic matrix. Thevarious applicable marking technologies may be photographic,xerographic, ink jet, electrophoresis, magnetographic, etc.

The electronic halftone generator has application to display purposeswhere additional dynamic range is needed and/or non-linearities inoutput brightness are difficult to compensate such, for example, asrequired in LED display systems, solid state matrix displays andspecialized multi-channel CRT's. The binary nature of the generatoroutput does not require linear transfer functions for displays ormarking technologies. All that is required of output devices is thatthey produce black or white (or appropriate colors in multi-colorapplications) displays.

The data compression aspect of halftones generation allows the deviceoutput to be combined with more conventional data compressiontechniques, providing reduced storage requirements, reduced transmissionbandwidths or run lengths and reduced transmitter power.

While the invention has been described with reference to its preferredembodiment, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the true spirit and scope of theinvention. In addition, many modifications may be made to adapt aparticular situation or material to the teaching of the inventionwithout departing from its essential teachings.

What is claimed is:
 1. Apparatus for converting an electrical analoginput signal representing an image into a corresponding output signal inthe form of a dot pattern corresponding to said image comprising:meansfor generating a time-varying electrical function which is a function offirst and second signals of first and second frequencies, respectively,said first and second frequencies being separately adjustable, means foraccepting said analog signal as a series of successive scan lines duringthe generation of each dot which will form said dot pattern, said analogsignal being produced by scanning said image in first and seconddirections, means coupled to said generating means and said acceptingmeans for comparing said successive scans with said function andgenerating a comparison signal when said function differs from saidsuccessive scans, means responsive to said difference signal forproviding an output signal, and means for generating said dot pattern byscanning said output signal in directions corresponding to said firstand second directions, the direction of alignment of the dots relativeto said first direction of scan being determined by the selection ofsaid first and second frequencies.
 2. The apparatus as defined in claim1 wherein said first and second signals have first and second amplitudesassociated therewith, said first and second amplitudes being separatelyadjustable in a manner wherein the shape of each dot in said dot patterncan be controlled.
 3. The apparatus as defined in claim 2 wherein saidfirst and second amplitudes further control the direction of chaining ofeach dot in said dot pattern in a manner such that the chainingdirection may be different than said alignment direction.
 4. Theapparatus as defined in claim 1 wherein said first and secondfrequencies are selected such that the alignment direction is differentfrom said first and second directions of scan.
 5. A method forconverting an electrical analog input signal representing an image intoa corresponding output signal in the form of a dot pattern correspondingto said image comprising the steps of:generating a time-varyingelectrical function which is a function of first and second signals offirst and second frequencies, respectively, said first and secondfrequencies being separately adjustable, accepting said analog signal asa series of successive scans during the generation of each dot whichwill form said dot pattern, said analog signal being produced byscanning said image in first and second directions, comparing saidsuccessive scans with said function and generating a comparison signalwhen said function differs from said successive scans, and providing anoutput signal, said dot pattern being generated by scanning said outputsignal in directions corresponding to said first and second directions,the direction of alignment of the dots relative to said first directionof scan being determined by the selection of said first and secondfrequencies.
 6. The method as defined in claim 2 wherein said first andsecond signals have first and second amplitudes associated therewith,said first and second amplitudes being separately adjustable in a mannerwherein the shape of each dot in said dot pattern can be controlled. 7.The method as defined in claim 6 wherein said first and secondamplitudes further control the direction of chaining of each dot in saiddot pattern in a manner such that the chaining direction may bedifferent than said alignment direction.
 8. The method as defined inclaim 5 wherein said first and second frequencies are selected such thatthe alignment direction is different from said first and seconddirections of scan.